Measures of Dispersion for Ungrouped Data

Question 9: The mean of the data 1, a, 2a, 8, 9 and 15 which has been arranged in ascending order is b. If each number of the data is subtracted by 3, the new median is 4 7 b . Find (a) The values of a and b, (b) The variance of the new … Read more

Question 7: A set of data consists of twelve positive numbers. It is given that Σ ( x− x ¯ ) 2 =600 and Σ x 2 =1032. Find (a) the variance (b) the mean Solution: (a) Variance= Σ ( x− x ¯ ) 2 N               = 600 12               =50 (b) Variance= Σ x 2 N − ( x ¯ ) … Read more

Question 5: A set of data consists of 9, 2, 7, x2 – 1 and 4. Given the mean is 6, find (a) the positive value of x, (b) the median using the value of x in part (a). Solution: (a) Mean=6 9+2+7+ x 2 −1+4 5 =6                      x 2 +21=30                             x 2 … Read more

Question 3: The mean of five numbers is p . The sum of the squares of the numbers is 120 and the standard deviation is 2q. Express p in terms of q. Solution: Mean  x ¯ = ∑ x N p = ∑ x 5 ∑ x = 5 p Standard deviation,  σ = ∑ x … Read more

Question 1: Given that the standard deviation of five numbers is 6 and the sum of the squares of these five numbers is 260.  Find the mean of this set of numbers. Solution: Given that  σ = 6 ,  Σ x 2 = 260. σ = 6 Σ x 2 n − X ¯ 2 = … Read more

Variance and Standard Deviation 1. The variance is a measure of the mean for the square of the deviations from the mean. 2. The standard deviation refers to the square root for the variance. (A) Ungrouped Data Example 1: Find the variance and standard deviation of the following data. 15, 17, 21, 24 and 31 Solution: Variance,  σ … Read more

(A) Interquartile Range of Ungrouped Data Example 1:  Find the interquartile range of the following data. (a) 7, 5, 1, 3, 6, 11, 8 (b) 12, 4, 6, 18, 9, 16, 2, 14 Solution: (a) Rearrange the data according to ascending order. Interquartile Range = upper quartile – lower quartile = 8 – 3 = 5  … Read more

(A) Range of Ungrouped Data Example 1: Find the range for the set of data 2, 4, 7, 10, 13, 16 and 18. Solution: Range = largest value – smallest value    = 18 – 2    = 16

8.2.1a Mean 1. The mean of the data is an average value obtained by using the formula: Mean= Total data values Number of data (A) Ungrouped Data Example 1 (a) Find the mean for the set of data 2, 4, 7, 10, 13, 16 and 18. (b) A value of xis added into the above set of data, the … Read more