the stem - and - leaf plot below shows the number of pages each student in a class read the previous…

Explanation:

Step1: Write out the data - set

The data - set from the stem - and - leaf plot is: 0, 0, 5, 8, 12, 13, 15, 18, 19, 22, 24, 26, 27, 27, 27, 33, 35, 36, 42, 44, 46, 57. There are (n = 22) data points.

Step2: Calculate the median

Since (n = 22) (an even number), the median is the average of the (\frac{n}{2}=11)th and ((\frac{n}{2}+1) = 12)th ordered data points. The 11th value is 24 and the 12th value is 26. So, the median (M=\frac{24 + 26}{2}=25).

Step3: Calculate the mode

The mode is the most frequently occurring value. The number 27 appears 3 times, more frequently than any other number, so the mode (Mo = 27). Since (25<27), the median is less than the mode.

Step4: Calculate the range

The range (R) is the difference between the maximum and minimum values. The maximum value is 57 and the minimum value is 0. So, (R=57 - 0=57\neq52).

Step5: Calculate the first quartile

The first quartile (Q_1) is the median of the lower half of the data. The lower half of the 22 - data - point set consists of the first 11 data points: 0, 0, 5, 8, 12, 13, 15, 18, 19, 22, 24. Since (n_1 = 11) (an odd number), the median of this set (i.e., (Q_1)) is the 6th value, which is 13.

Step6: Check for symmetry

The data is not symmetric. The left - hand side of the data has more values clustered around the lower numbers, and the right - hand side has a long tail towards the higher numbers.

Answer:

The value of the first quartile is 13.