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Form 4 Mathematics Statistics II Questions and Answers
Determine the interquartile range for the following set of numbers: 4,9,5,4,7,6,2,1,6,7,8,
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1.
For a sample of 100 bulbs the time taken for each bulb to burn out was recorded. The table below shows the results of the measurements. Using an assumed mean or otherwise,calculate i).The mean ii).The standard deviation of the distribution.
2.
The table below gives marks scored by 80 candidates in a test. Using assumed mean of 25.5 calculate the mean, the variance and the standard deviation of the marks.
3.
The table below shows distribution of marks scored in a test by standard 8 pupils in one school. Using 57 as the assumed mean mark, calculate (a)the actual mean for the grouped marks. (b)the standard deviation of the marks.
4.
Determine the interquartile range for the following set of numbers: 4,9,5,4,7,6,2,1,6,7,8,
5.
Five pupils A,B,C,D and E obtained the marks 53,41,60,80 and 56 respectively. The table below shows part of the work to find the standard deviation. (a) Complete the table (b) Find the standard deviation.
6.
In an agricultural research centre , the lengths of a sample of 50 maize cobs were measured and recorded as shown in the frequency distribution table below.
7.
The marks obtained by 10 pupils in an English text were 15,14,12,13,p,16,11,13,12 and 17. The sum of the squares of the marks, #sum x 2# is 1,794. (a) Calculate the: (i)value of p (ii) Standard deviation (b) If each marks is increased by 3,write down the : (i)new mean (ii)new standard deviation.
8.
The masses of 40 babies in a certain clinic were recorded as follows: Calculate: (a) The interquartile range of the data. (b) The standard deviation of the data using 3.45 as the assumed mean
9.
The table below shows the ages in tears of 60 people who attended a conference. Calculate: (a)the interquartile range of the data (b)the percentage of the people in the conference whose ages were 54.5 years and below
10.
The data below represents the ages in months at which 6 babies started walking: 9,11,12,13,11 and 10. Without using a calculator,find the exact value of the variance of the data.
11.
The heights in centimeters of 100 tree seedlings are shown in the table below. Find the quartile deviation of the heights.
12.
A basketball team scored the following points in 6 Matches:10,12,14,16,28 and 30. Using an assumed mean of 15,determine the standard deviation correct to 2 decimal places.
13.
The mass in kilograms of 9 sheep in a pen were: 13,8,16,17,19,20,15,14 and 11. Determine the quartile deviation of the data.
14.
The table below shows frequency distribution of heights of 40 plants in a tree nursery.(a) State the modal class. (b) Calculate: (i)the mean height of the plants (ii)the standard deviation of the distribution (c) Determine the probability that a plant taken at random has height greater than 40 cm.
15.
The heights of 40 athletes in a country competition were as shown in the table below. (a) Find the value of x (b) State the modal class. (c) Calculate: (i) The mean of the athletes (ii) The median height, correct to 1 decimal place, of the athletes.
16.
The table below shows the life expectancy in hours of 106 bulbs. (a) Calculate the mean life frequency. (b) On a grid draw a cumulative frequency curve and use it to determine the median.
17.
The table below shows high altitude wind speeds recorded at a weather station in a period of 100 days. (a).On the grid provided draw a cumulative frequency graph for the data. (b).Use your graph to estimate i).interquartile. ii).the number of days when the wind speed exceeded 125 knots.
18.
Length of 100 mango leaves from a certain tree were measured to the nearest centimeters and recorded as per the table below.
19.
The table below gives the marks obtained in a mathematical test by 47 candidates. (a) Calculate the mean score (b) Draw a cumulative frequency graph and use it to estimate (i)the median score (ii)the semiinterquartile range.
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