Question

The following scores were received on a recent exam. there were 100 questions asked and 1 point was awarded for each question answered correctly. No partial credit was allowed.

98, 84, 89, 81, 50, 98, 72, 79, 68, 81, 85, 86, 90, 84, 77, 71, 70, 86, 81, 71, 84, 86, 85, 85, 94

a) based on the above data, construct a frequency distribution table incorporating each value ( ie. no grouped frequencies) containing absolute frequencies, relative frequencies, cumulative frequencies and cumulative percentages

b) compute the mode, median and mean for this distribution. which measure of central tendency would you be inclined to use for this distribution and why ?

c) make a graphic presentation of the above distribution. be sure to appropriately label the x and y axis with what is being measured.

d) be sure to describe the skewness of this distribution.

e) what specific type of univariate graphic presentation would you be inclined to use ? why ?

Answer 1

SOLUTION A:

b) MEAN= 2035/25= 81.4

MEDIAN: n= 25 ODD

so on arranging data on ascending order we have

{(n+1)/2}th observation will be median which is (25+1)/2= 13th observation

MEDIAN=84

MODE =81(MOSTLY OCCURRED VALUE)

I will use median for measure of central tendency because data is skewed.

c) By using SPSS we have

d) From Histogram we can say data is NEGATIVELY skewed. It has a large number of occurrences of values in the upper value side and few in the lower values side.

e) Histogram because this will easily let us know that weather data is skewed or not. We can easily know if data is UNIMODAL OR BIMODAL (having two modes)