Question

. A study was conducted to examine the correlation between number of study hours and students grads in exam. Study hours for students: 2, 3, 5, 6, 8, 10, 10, 2, 5, 6, 5, 3, 7, 6, 2, 7, 6, 8, 2, 5 Grads in exam for students: 3, 4, 6, 7, 8, 10, 9, 8, 3, 6, 5, 4, 6, 6, 3, 7, 6, 3, 4, 5 1- as ungrouped data find the frequency, accumulated relative frequency, and accumulative relative frequency for study hours. 2- Frequency Polygon for study hours. 3- percentile graph for study hours. 4- determine whether the data for study hours are normally distributed with explanation. 5- determine whether the data for study hours are uni-modal, bimodal, or multimodal. 6- scatter and plot diagram

Answer 1

We have given data for study hours and grades. For that, We need to do calculations based on study hours,

1- as ungrouped data find the frequency, accumulated relative frequency, and accumulative relative frequency for study hours.

Study Hour	Freq	Cumulative frequency	Relative frequency
2	4	4	0.20
3	2	6	0.30
5	4	10	0.50
6	4	14	0.70
7	2	16	0.80
8	2	18	0.90
10	2	20	1.00
Total	20

2- Frequency Polygon for study hours.

For this diagram we plot the study hours in x-axis and frequency in the y-axis and join by a line, we get the below curve

3- percentile graph for study hours

to make this we made,

1=minimum study hour

2=25% percentile study hour

3=50% percentile study hour

4=75% percentile study hour

5=maximum study hour

and plot them in y-axis we get,

4- determine whether the data for study hours are normally distributed with explanation

As per the frequency plot by polygon shows that there is no symmetric pattern which is required for normality for a distribution. Hence we can say that the above data is not normal. Also, the data has more than one mode.

5- determine whether the data for study hours are uni-modal, bimodal, or multimodal

Here modal means how many highest frequency the data observed, as a result we can see that 3 modes (2,5,6 study hours).

Hence the data has 3 modes so it is multimodal data.

6- scatter and plot diagram

Plotting study hour in x-axis and Grades in y-axis as below,