Data Analytics
4. The final grades of 80 mathematics students are recorded in the following table:
68 73 61 66 96 79 65 86 84 79 65 78 78 62 80 67 75 88 75 82 89 67 73 73 82 73 87 75 61 97 57 81 68 60 74 94 75 78 88 72 90 93 62 77 95 85 78 63 62 71 95 69 60 76 62 76 88 59 78 74 79 65 76 75 76 85 63 68 83 71 53 85 93 75 72 60 71 75 74 77
a) Create a Histogram and describe it.
b) Find the lowest grade.
c) Find the highest grade.
d) Find the sample mean or average.
e) Find the median.
f) Calculate the standard deviation.
g) Show the Five Number Summary
h) Create the appropriate graph to show the 5 number summary.
Sample Solution
a) Histogram: The histogram shows the frequency of the grades obtained by 80 mathematics students. The x-axis represents the various grades, ranging from 53 to 97, while the y-axis showshow many students achieved each grade. Most of the students scored between 65 and 90, with a peak at 75. There are very few scores below 60 and above 95.
b) Lowest Grade: 53
c) Highest Grade: 97
d) Sample Mean or Average: 76.2125
e) Median: 77
f) Standard Deviation: 12.2071
g) Five Number Summary: Minimum = 53; Q1 = 65; Median (Q2) = 77; Q3 = 85; Maximum = 97
h) The appropriate graph to show this 5 number summary is a Box Plot which displays five key values (Minimum, Maximum, First Quartile (Q1), Third Quartile(Q3), and Median). The horizontal line in the box plot divides it into two sections - upper section depicting higher half data points and lower section depicting lower half data points. On either side of this line lies two dotted lines called whiskers indicating variability outside quartiles including outliers if present in data set . An outlier is an observation that's far away from other observations. In this case there are no outliers since all observations are clustered together tightly around 76 marks with only small variations up & down throughout distribution either side of median point 77 marks which is visible as central vertical solid line in box plot diagram here along with quartiles shown as left&right boundaries for both halves respectively .