Statistical Methods-Question and Answer
Measures of Dispersion and Position
1. The following data give the number of shoplifters apprehended during each of the past eight
weeks at a large department store.
1 7 3 1 51 26 1 1
a. Find the mean for these data. Calculate the deviations of the data values from the
mean. Is the sum of these deviations zero?
𝑠𝑢𝑚 1+7+3+1+51+26+1+1 91
𝑥̅ = = = = 11.375 ≈ 11.38
𝑛 8 8
Therefore, the mean for this set of data is 11.375 ≈ 11.38
Table1. Deviation of Shoplifters
𝒙 𝒙𝟐
𝟏 1 − 11.38 = -10.38
𝟕 7 − 11.38 = -4.38
𝟑 3 − 11.38 = -8.38
𝟏 1 − 11.38 = -10.38
𝟓𝟏 51 − 11.38 = 39.62
𝟐𝟔 26 − 11.38 = 14.62
1 1 − 11.38 = -10.38
1 1 − 11.38 = -10.38
∑ = (𝑥 − 𝑥̅ ) = 0.04 ≈ 0
b. Calculate the range, variance, and standard deviation.
In (1, 7, 3, 1, 51, 26, 1, 1) the lowest number of shoplifter at a large department store is 1 and
the highest is 51.
Range = Highest Number – Lowest Number
= 51 − 1
= 50
Therefore, the range for this set of data is 50.
Measures of Dispersion and Position
1. The following data give the number of shoplifters apprehended during each of the past eight
weeks at a large department store.
1 7 3 1 51 26 1 1
a. Find the mean for these data. Calculate the deviations of the data values from the
mean. Is the sum of these deviations zero?
𝑠𝑢𝑚 1+7+3+1+51+26+1+1 91
𝑥̅ = = = = 11.375 ≈ 11.38
𝑛 8 8
Therefore, the mean for this set of data is 11.375 ≈ 11.38
Table1. Deviation of Shoplifters
𝒙 𝒙𝟐
𝟏 1 − 11.38 = -10.38
𝟕 7 − 11.38 = -4.38
𝟑 3 − 11.38 = -8.38
𝟏 1 − 11.38 = -10.38
𝟓𝟏 51 − 11.38 = 39.62
𝟐𝟔 26 − 11.38 = 14.62
1 1 − 11.38 = -10.38
1 1 − 11.38 = -10.38
∑ = (𝑥 − 𝑥̅ ) = 0.04 ≈ 0
b. Calculate the range, variance, and standard deviation.
In (1, 7, 3, 1, 51, 26, 1, 1) the lowest number of shoplifter at a large department store is 1 and
the highest is 51.
Range = Highest Number – Lowest Number
= 51 − 1
= 50
Therefore, the range for this set of data is 50.
