Question

Given the following scores: 62,64,65,68,70,72,72,75,75,75,76,78,81,83, 83,84,85,87,88,92,95 a. What is the mode? b. Construct a histogram c. Construct a stem plot identifying outliers d. Would you describe the scores as more skewed or symmetric

Answer 1

a)

Mode : In the given data, the observation 75 occurs maximum number of times (3) .. Z= 75

b)

Step 1: Deciding the number of categories:
# of classes = root(n), where n is the number of entries;
                        = root(21) = 5

Step2: Determining the indivisuals per classes:
Class   Interval   Freq.   %
-----------------------------------------------------
1               [62, 68.6)   4   19.048%
2               [68.6, 75.2)   6   28.571%
3               [75.2, 81.8)   3   14.286%
4               [81.8, 88.4)   6   28.571%
5               [88.4, 95)   2   9.524%

Step3: Find the density for each class:
Class     Base       (%)       Height(density)
---------------------------------------------------------
1               6.6   19.048%   2.886
2               6.6   28.571%   4.329
3               6.6   14.286%   2.165
4               6.6   28.571%   4.329
5               6.6   9.524%   1.443

Step4: Plot the Histogram.

29 29 19 14 1 62 8.6 5.2 1.8 8.4 明

c)

Stem Leaf Count 62458 4 702 2 5 5 5 6 8 8 7 8 1334 5 7 8 925 2 Basic Statistics values : Count 21 Minimum 62 Maximum 95 Sum 1630 Mean 77.619 Median 76 Mode 75 Standard Deviation 9.21 Variance 84.75

d)

median is less than mean Hence the scores are skewed to left.