STATISTICS. 1. Measures of Central Tendency

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1 STATISTICS 1. Measures o Central Tendency Mode, median and mean For a sample o discrete data, the mode is the observation, x with the highest requency,. 1 N F For grouped data in a cumulative requency table, the median = L C m where L is the lower boundary o the median class N is total requency F is the cumulative requency beore the median class C is the interval o the median class m is the requency o the median class x x The mean is the average o all the observations. Hence, x. For grouped data, x. N (a) Find the mode, median and mean or, 3, 1,, 6, 8, 9, 3,, 3. (b) Find the mode, median and mean or the data in the table below. Score Frequency (c) [Mode =, Median = 3, Mean = 4] Find the modal class and calculate the median and mean or the data in the table below. Points requency [Mode = 4, Median = 6, Mean = 7.] (d) Find the modal class and calculate the median and mean or the data in the table below. Marks [Modal class = 10-14, Median = 10.75, Mean = 10.33] [Modal class = 46-60, Median = 48.15, Mean = 46.53] Statistics 1

2 (e) Estimate the mode and calculate the median and mean or the histogram below. () Estimate the mode and calculate the median and mean or the histogram below. [Mode = 7.8, Median = 7.71, Mean = 7.6] Statistics [Mode = 15.5, Median = , Mean = 149.1]

3 (g) Find the modal class and ind the median and mean or the ogive below. (h) Find the modal class and ind the median and mean or the ogive below. [Modal class = 15-19, Median = 17.6, Mean = 18.65] [Modal class = 45-49, Median = 49.5, Mean = 50.5] Statistics 3

4 . Measures o Dispersion: Range, quartiles, interquartile range, variance and standard deviation. The range o a sample is the dierence between the observations with the highest value and the lowest value. 1 1 N F The irst quartile, Q 1 = L 4 Q C 1 Q1 and the third quartile, Q = N F 4 3 LQ 3 CQ Q1 3 Q3 Interquartile range = Q 3 Q 1. It should be recognised that the median is Q. The variance, x x x N N x or discrete data. x x x For grouped data, x. The standard deviation is actually variance x x x For discrete data, x. N N x x x For grouped data, x. (a) Find the range and the interquartile or 5, 1,, 3, 4, 6, 3, 8,, 5, 9. (b) Find the range and the interquartile range or 1, 17, 13, 19, 15, 8, 1, 11. (c) [Range = 8, Interquartile range = 4] Find the range and the interquartile or Score Frequency (d) [Range = 11, Interquartile range = 4.5] Find the range and the interquartile range or Points No. o person 3 5 [Range = 8, Interquartile range = 4] Statistics 4 [Range = 6, Interquartile range = 3]

5 (e) Find the interquartile range or the table below. Marks No. o Students () Find the interquartile range or the table below. Age (year) No. o residents (e) [Interquartile range = marks] Calculate the interquartile range or the ogive below. () [Interquartile range = 8.95 years] Calculate the interquartile range or the ogive below. [Interquartile range = 1.5 mm] Statistics 5 [Interquartile range = 6.5 years]

6 (g) Calculate the interquartile range or the histogram below. (h) Calculate the interquartile range or the histogram below. [Interquartile range = 5.95 kg] [Interquartile range = minutes] Statistics 6

7 (a) Find the mean, variance and the standard deviation or the data below. 5, 1, 6, 3, 6, 10. (b) Find the mean, variance and the standard deviation or the data below. 18, 1, 16, 11, 19, 18, 1, 14. (c) [Mean = 7, = 9.333, = 3.055] Complete the table below and calculate the x x x x x x x (d) [Mean = 15, = 7.5, =.739] Complete the table below and calculate the x x x x x x x [Mean = 7, = 9.333, = 3.055] [Mean = 7., = 10.66, = 3.65] Statistics 7

8 (e) Complete the table below and calculate the Class x () Complete the table below and calculate the Class x x x [Mean = 8.75, = , =.981] (g) Complete the table below and calculate the Class x [Mean = 7.5, = 101, = 10.05] (h) Complete the table below and calculate the Class x x x [Mean = 1.4, = 0.64, = 4.543] [Mean = 37.5, = 376, = 19.39] Statistics 8

9 (i) (j) Extract the data rom the histogram above and complete the table below. Calculate the mean, variance and the standard deviation or Extract the data rom the histogram above and complete the table below. Calculate the mean, variance and the standard deviation or Class x Class x [Mean = 55.55, = , = 6.453] [Mean = 150.3, = 17.36, = 13.13] Statistics 9