Question

¡Students answered SAT-type questions without seeing the passage on which the questions were based. The data is below:

§54, 52, 51, 50, 36, 55, 44, 46, 57, 44, 43, 52, 38, 46, 55, 34, 44, 39, 43, 36, 55, 57, 36, 46, 49, 46, 49, 47

¡Plot a frequency distribution for these data

¡Create a histogram

¡What is the general shape of the distribution?

¡Create a stem-and-leaf for the data

¡If students just guess, they would have been expected to earn a score of approximately 20. Do these students appear to do better than chance even when they haven’t read the passage

Answer 1

(i)

From data set we have

Minimum value = 34

Maximum value = 57

Let us assume number of classes 5 so class width will be

Class width = (57-34) / 5 = 4.6

That is class width is 5.

Following table shows the frequency distribution:

Classes Frequency 34-39 39-44 44-49 49-54 54-59 Total 2 2 28

(ii)

Following is the histogram:

(iii)

Right tail is approximately same as left tailed so distribution seemed to be approximately symmetric. The distribution is unimodal.

(iv)

Following is the stem and leaf display:

(v)

No because 20 is less from all the data values.