Question

The Harleys Daycare. decided to use 20 different water balloon categories. Their prices (on 100 units) are listed below:

27           25           10           7              13           20           27           15           25           10          

22           16           11           9              12           20           17           17           23           20

a. Construct a grouped frequency distribution with 6 classes.           

Step 1. Find Range

Step 2. Given the number of classes, the width of each class is

Step 3. Create class boundaries

Step 4. Find the numerical frequencies

b. Use Excel to construct a Histogram. (Tools à Data Analysis à Histogram à for the input range, select the given values, for the bin range select the classes upper boundaries values à check Chart Output)

Note: If you don’t have the capability of using excel for the histogram, draw one by hand.

[D(14 points)] Consider the following set of data containing the amount of paid tuition/week for part-timers:

Child Name	Amount	Z-Score
Marie	70
Philip	80
John	55
Isabela	75
Raymond	55
Richard	75
Edgar	80
Jerry	85
Christiana	60
Juliet	85

Z = ( X – U)/ σ where u is the mean and σ is the standard deviation.

a. For the set of data given above, calculate the following descriptive statistics (Briefly explain, especially the quartiles calculations. Use the rules given in the homework 2). For the rest you can use excel tools as long as you show your work.

Mean	2.71
Median	2
Mode	2
Who is in the lowest quartile? Explain	Q1 = 1 Quartile 1 is the median of the lower half of the data.
Who is in the uppermost quartile?	Q3 = 5 Q3 is the median of the upper half of the data.
Interquartile Range	Interquartile range = q3 – q1 = 5 – 1 =
Range	Range = highest value – lowest value = 9
Standard Deviation	2.49
Variance

b.   Compute the z-scores and enter them in the first given table. Give the formula you used.

c.   What type of skewness does this data set have? The data set has a left tail skewness.

Answer 1

#1 )

First we need to arrange the data set in ascending ( increasing order )

Step 1 : Range = Maximum value - Minimum value

= 27 - 7

Range = 20

Step 2 : We are asked to construct 6 classes

Class width = Range / number of classes

= 20/ 6

= 3.33 ~ 4

So Class width = 4

Step 3 : Class boundaries

First we need to construct class intervals ( lower and upper )

The Minimum value is 7, therefore lower class interval of first class would be 7

To find the lower bound of 2nd class interval, we need to add class width 4 to 7 , so 4+7 = 11

Similar way we need to go on adding the class width to get the lower class intervals of next class

Lower class intervals are 7,11,15,19,23,27

To find the upper class interval of first class we need to subtract 1 from the lower class interval of the 2nd class 11

So 11 - 1 = 10 and then to find the next upper class intervals we need to go on adding the class width 4

Upper class intervals are 10,14,18,22,26,30

To find the class boundaries we need to subtract 0.5 from lower class intervals and add 0.5 to upper class intervals

Step 4 and part b) : Frequency and Histogram using excel

Go to Data menu ---> Data analysis ---> Histogram

Then for input range select the given data set arranged in ascending order .

For Bin range select the Upper class boundaries ( without heading )

Check the box for Chart output to get the histogram.

Click on OK.

The frequency table will be appear with the Bar chart:

Frequency table :

Bar chart :

To get the histogram from the bar chart , click on any bar and then right click

Then select "Formal data point" option

Set Gap width = 0%

The final histogram will be appear as follows