# Form 2 Mathematics Statistics I Questions and Answers

This course contains worked out Form 2 Mathematics Statistics I questions.

Lessons (**56**) * SHARE*

- 1.
The shoe sizes for 40 pupils in a class were recorded as shown in the table below. Determine the mean shoe size in the class.

3m 21s - 2.
The height in centimeters of 60 children attending clinic were recorded as follows: Calculate the median height.

6m 50s - 3.
The mean age of 15 boys in a class is 19 years. On a day when one of the boys was absent, the rest gave their ages as follows: 20,22,16,18,17,21,18,20,17, 18,19,20,19,21. Find the age of the absent boy.

3m 9s - 4.
Every week the number of absentees in a school was recorded. This was done for 39 weeks. The observations were tabulated as shown below: Estimate the median absence rate per week in the school.

5m 34s - 5.
The following enrolment figures for twenty primary schools were collected 934 923 936 931 924 933 933 937 926 923 934 931 929 934 927 927 932 934 927 940 a) Determine the mode. b) The differences from an assumed mean were
obtained and rearranged as follows: -2 -2 -1 1 2 2 2 4 6 6 7 8 8 9 9 9 9 11 12 15 I. Determine the assumed mean. II. Use the assumed mean in (b)

13m 42s - 6.
Six weeks after planting, the height of bean plants were measured correct to the nearest centimeter. The frequency distribution is given in the table below. (a) Enter the cumulative frequency values in the table above. (b) Estimate the median height of the plants.

4m 52s - 7.
The number of people who attended n agricultural show in one day was 510 men, 1080 women and some children. When the information was presented on pie chart, the combined angle for the men and children was 2160. Find the angle representing the children.

6m 13s - 8.
Patients who attend a clinic in one week were grouped by ages as shown in the table below. Estimate the mean age.

4m 18s - 9.
The table below shows height of 50 students. (a) State the modal class. (b) Calculate the median height.

5m 44s - 10.
The frequency distribution table below shows the weekly salary (K£) paid to workers in a factory. On the grid provided below, draw a histogram to represent the information shown above.

8m 58s - 11.
The table below shows the number of goals scored by a football team in 20 matches. Find: (a) The mode (b) The mean number of goals.

2m 56s - 12.
The following data was obtained for the masses of certain animals. Complete the histogram on the grid provided below.

4m 16s - 13.
The marks scored by a group of pupils in a mathematics test were recorded in the table below. (a) (i) State the modal class. (ii) Determine the class in which the median mark lies (b) Using an assumed mean of 54.4, calculate the mean mark.

12m 19s - 14.
The histogram shown below represents the distribution of heights of seedlings of a certain plant. The shaded area in the histogram represents 20 seedlings. Calculate the percentage number of seedlings with heights of at least 23 cm but less than 27 cm.

2m 37s - 15.
The frequency distribution table below represents the number of Kilograms of meat sold in a butchery. (a) State the modal frequency (b) Calculate the mean mass (c) Calculate the median mass

7m 44s - 16.
The masses of people during a clinic session were recorded as shown in the table below. Calculate the mean mass.

4m 36s - 17.
The table below shows the height, measured in the nearest cm, of 101 pawpaw trees. (a) State the modal class. (b) Calculate to 2 decimal places: (i) The mean height; (ii) The difference between the median height and the mean height.

10m 24s - 18.
The masses in kilograms of 20 bags of maize were; 90, 94, 96, 98, 99, 102, 105, 91, 102,99,105,94,99,90,94,99,9 8,96,102 and 105 Using an assumed mean of 96kg, calculate the mean mass, per bag, of maize.

7m 47s - 19.
The product of milk, in litres, of 14 cows on a certain day was recorded as follows: 22, 26, 15, 19, 20, 16, 27, 15, 19, 22, 21, 20, 22 and 28. Determine: (a) the mode; (b) the median

4m 53s - 20.
The lengths, in cm, of pencil used by pupils in standard one class on a certain day were recorded as follows. 3 7 9 9 20 14 10 6 8 13 14 3 17 13 8 12 5 15 14 15 7 12 11 6 10 19 9 14 6 9 10 16 13 9 12 11 10 7 10 11 a) Using a class width of 3, and starting with the shortest length of pencil, make a frequency distribution table for the data.

5m 58s - 21.
The table below shows the frequency distribution of marks scored by student in a test. Determine the median mark correct to 2 s.f.

3m 54s - 22.
The masses, in kilograms, of patients who attended a clinic on a certain day were recorded as follows. 38 52 46 48 60 59 62 73 49 54 49 41 57 58 69 72 60 58 42 41 79 62 58 67 54 60 65 61 48 47 69 59 70 52 63 58 59 49 51 44 67 49 51 58 54 59 39 59 54 52 a) Starting with the class 35-39, make a frequency distribution table for the data. b) Calculate: (I) the mean mass (ii) the median mass

8m 6s - 23.
A test given to 40 students produced the following results:
5 students got grade A.
12 students got grade B.
15 students got grade C.
5 students grade D.
3 students got grade E.
(a) Show the above information on a pie chart.
(b) Find the percentage which represents:
(i) those with grade A.
(ii) those with grade C and D.

3m 32s - 24.
The following table shows the number of trees planted in a certain farm:
Represent the information on a bar graph.

2m 23s - 25.
The table below shows the importation of vehicles (in thousands) for the year 1994 to 2002.
Draw a line graph to represent the information.

2m 12s - 26.
The heights, to the nearest centimetre, of 20 boys and 20 girls were measured and recorded as follows:
(a) Construct a histogram for each of the above data, using 115 — 119 as the first class for both boys and girls.
(b) Construct frequency polygons of the data on the same axes.

7m 57s - 27.
The data below shows the population of Matunya Secondary School.
Draw a pictogram to represent this information.

2m 3s - 28.
The table below shows the number of letters collected from the post office by a school driver during school year:
Draw a frequency polygon to represent the data.

2m 21s - 29.
The number of pupils present in a class for 20 school days were:
(a) Make a grouped frequency table with 24-26 as the first class.
(b) Draw a bar-graph to represent the information.
(c) Draw a histogram to represent the information.

5m 26s - 30.
Pupils in a class in a certain day school were asked how they travelled to school. They gave the following information:
Draw a pie-chart to represent this data.

2m 18s - 31.
The examination marks in a mathematics test for 72 students were as follows:
Using class interval of 10 and starting from 10-19, make a frequent distribution table. Use the table to:
(a) Find the modal class.
(b) Estimate:
(i) the mean.
(ii) the median.

10m 25s - 32.
The heights, to the nearest centimetre, of 50 students in a particular school were as follows:
(a) Using class interval of 10 and 135 - 144 as the first class, make a frequency distribution table.
(b) From the table:
(i) state the modal class.
(ii) estimate the median and the mean.

9m 14s - 33.
The population in thousands of 42 districts were recorded as follows:
Make a grouped frequency distribution table with the first class as 85-94 and from it:
(a) find the modal class.
(b) estimate the mean and the median.

12m 53s - 34.
In a Kiswahili test, 40 students scored the following marks:
Group the above data using class intervals of size 5 and 25-29 as the first class. Hence, estimate the mean and the median. State also the modal class.

10m 20s - 35.
The data below shows masses of fish in kilogrammes caught by fishermen in one day.
Estimate the mean and the median, and state the modal class.

6m 21s - 36.
The number of words which could be read per minute by 80 candidates in an examination is shown in the table below.
Estimate the mean and the median, and state the modal class.

5m 41s - 37.
The diameters, to the nearest millimetre, of 78 bolts is as shown below.
Estimate the mean and the median, and state the modal class.

5m 54s - 38.
The amount in shillings, of pocket money given to students of a particular school is as shown below.
Estimate the mean and the median, and state the modal class.

6m 21s - 39.
The information below represents scores of 40 candidates in an aptitude test:
By using groups 10-14, 15-19, 20-24, ...:
(a) determine the modal class.
(b) estimate the mean and the median.

9m 44s - 40.
The data below represents times in seconds recorded in the heats of a 100 m race during an athletics meeting:
By using groups of 11.5-11.9, 12.0-12.4 ..., make a frequency distribution table for the above data and hence:
(a) determine the modal class.
(b) estimate the mean and median.

9m 11s - 41.
The data below represents marks scored by 10 students in a test. Find the mean, mode and the median of the marks:
7, 8, 9, 14, 13, 5, 10, 9, 11, 6

1m 48s - 42.
Forty eight pupils gave the number of children in their homes as follows:
(a) Make a frequency distribution table for the data.
(b) Determine the mode.
(c) Calculate the mean number of children.

5m 22s - 43.
Twenty pupils in a class measured their masses and recorded them to the nearest kilogramme as below:
40 48 56 52 49 57 56 52 53 48
38 39 43 47 41 60 63 59 45 51
Make a distribution table and find the mean and the mode.

5m 5s - 44.
The classes in a primary school had the following number of pupils:
42 45 48 40 46 42 44 48 39 40 42
41 47 46 45 49 45 42 40 38 39
46 47 42 40 41 43 44 45 46 48
(a) Make a frequency distribution table.
(b) Determine the mode.
(c) Calculate the mean.

4m 38s - 45.
In an experiment to measure the length, in centimetres, of an exercise book, 16 students recorded the following:
12.8 12.5 13.4 13.6 13.5 14.5 15.2 11.8
14.5 13.9 13.7 14.4 14.4 14.3 15.3 14.7
Construct a frequency table and use it to determine the mean and the mode.

4m 45s - 46.
A sample of 40 nuts Were picked at random from a factory and their diameters measured to the nearest 0.1 mm as below:
20.4 20.5 10.1 10.2 20.3 20.0 19.9 19.9
20.6 20.5 20.4 20.3 20.1 20.9 20.2 20.3
20.3 20.4 20.1 20.1 20.8 20.7 20.5 20.4
20.0 20.1 20.5 20.6 20.7 20.1 20.0 19.8
20.3 20.4 19.9 20.0 21.0 20.9 20.8 20.4
(a) Prepare a frequency distribution table

8m 25s - 47.
In an athletics competition held in Kericho district, 12 athletes ran the 400 m race and their times in seconds were recorded as below:
58.2 54.2 49.8 52.3 55.6 50.8
53.8 51.9 50.7 52.3 57.2 52.3
Find the mean, mode and median.

3m 8s - 48.
The height in metres of 50 children wen recorded as follows:
Make a frequency table and from it determine the mean, the mode and the median.

12m 43s - 49.
The following frequency distribution table represents masses in kilogrammes of children in a class:
Find the mean, mode and median

3m 38s - 50.
The volume of milk (to the nearest 0.01
*l*) in 24 tetrapaks was measured and recorded as below: Find the mean, mode and median

4m 37s - 51.
The table below shows the duration, to the nearest minute, of telephone calls through an exchange:
Find the mean, mode and median

3m 21s - 52.
In an examination, the mean mark for Form 2B, in which there were 34 students, was 51. Form 2A, in which there were 36 students, had a mean of 42 marks. Calculate (to 1 dec. place) the mean mark for the two classes combined.

1m 49s - 53.
The mean of the numbers 3, 4, a, 5, 7, a, 5, 8, 5 and 9 is equal to the mode. Find the value of a and hence the median of the data.

2m 50s - 54.
The mean age in a Form II class of 36 boys was 16 years 8 months. lf an 18-year-old boy later left the class, what was the new mean age for class?

1m 33s - 55.
Forty five pupils in a mixed class sat for a mathematics test. The mean mark for the 25 girls in this class was 58.5 while the mean mark for all the pupils was 60.2. Calculate the mean mark for the boys

2m 3s - 56.
The mean height of five girls was found to be 148 cm. When a sixth girl joined the group, the mean height was reduced by 3 cm. Find the height of the sixth girl.

1m 12s

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