Question

The following scores represent the final examination grades for an elementary statistics course: 23 60 79 32 57 74 52 70 82 36 80 77 81 95 41 65 92 85 55 76 52 10 64 75 78 25 80 98 81 6
a. Construct a stem-and-leaf plot for the examination grades in which the stems are 1, 2, 3, . . . , 9.
b. Construct a relative frequency histogram, draw an estimate of the graph of the distribution, and discuss the skewness of the distribution.
c. Compute the sample mean, sample median, and sample standard deviation.

Answer 1

Answer:

a)  The decimal point is 1 digit(s) to the right of the |

  0 | 6

 1 | 0

 2 | 35

 3 | 26

 4 | 1

 5 | 2257

 6 | 045

 7 | 0456789

 8 | 001125

 9 | 258

b) The relative frequency histogram as attached diagram.

As shown, the plot is skewed to the left.

c)

i) mean = 62.7

ii) median = 72

iii) Standard deviation = 24.87923

Step-by-step explanation:

a) The first approach is to sort the data in ascending or descending order. Next, we Identify the minimum grade and the maximum grade. We then list the stems based on the minimum and maximum. And we construct the stem and leaf diagram as show. The first digit represents the stem and the last digit represents the leaf.  

As shown, all the grade are two digits value, with minimum as 06 and maximum as 98. In this case, the first stem is 0 and the last stem is 9.

Others (b & c) are just the usual calculations.