1. Some members of a class took a test. The scores were

summarized in the following frequency distribution. Find the mean, median, mode, upper and lower quartiles the interquartile range and the standard deviation of the scores and draw the histogram.

To find the mean, we add up all the scores and divide by the number of scores. The two 90s will add up 2x90 etc

To get the mean, we divide the total of the score by the number of scores, which is the sum of the frequencies

To get the median, we divide the scores into the upper half of the scores and the lower half. Since there are 10 scores, the upper half will be the top 5 scores and the lower half will be the lower 5 scores. The top 5 scores are the 80s and 90s. The bottom 5 scores are the 70 and the 60s. The median will be halfway between 70, which is the top of the bottom 5 scores, and 80 which is the bottom of the top 5 scores. The number which is halfway between 70 and 80 is

75

The mode is the most common score. It is

60

The upper quartile is the median of the upper half of the scores. Since there are 5 scores in the upper half, the median would be the third score which would be one of the

80

The lower quartile would be the median of the lower half of the scores. There are 5 scores in the lower half, and 4 of them are 60s, so the third one would be a

60

The interquartile range is the difference between the upper and lower quartiles

80 - 60 = 20

To get the standard deviation, we first find the deviations of all the scores.

Next square all the deviations.

To total up the squares of the deviations, we need to take the frequencies into account.

To get the variance which is the mean of the squares of the deviations, we divide the sum of the squares of the deviations by the number of scores.

variance = 1410/10 = 141

The standard deviation is the square root of the variance or

11.874342087

The histogram looks like