Question

4. Here is the data from last semester on what people spent on their last meal.

10.30   23.00   8.08     0.00     8.21     10.00   30.00   5.40     19.56   20.81   25.00   12.40   75.00   7.03     20.00   9.75     35.00   15.00   24.00   25.00   00.0            7.00     20.00   15.00   22.00   0.00     32.00   10.00   14.00   15.00   3.00     10.66   11.25   18.00   19.48   40.00   0.00     12.00   25.00   23.00   30.00            15.00

Construct a grouped frequency table. Use an interval number of 15.

What information has this table allowed you to extract?

What is the percentile rank of spending 30 dollars on a meal?

What is the score at which 80% of the participants spent less than?

What is the interquartile range for this data? (How do you find this?)

What is the mean, median and mode for this data?

Compute the variance and standard deviation for this data. (How do you find this?)

Answer 1

c) the percentile rank of spending 30 dollars on a meal is 88.095

d)   the score at which 80% of the participants spent less than, for this Z score corresponding to 0.8 is 0.841

Z=X-mu/sigma

Z*sigma= X-mu

0.841*13.38= X-17.28

11.25= X-17.28

X= 28.53 is  the score at which 80% of the participants spent less than.

E) 42 is the number of observations. 0.00,0.00,0.00,0.00,3.00,5.40,7.00,7.03,8.08,8.21,9.75,10.00,10.00,10.30,10.66,11.25,12.00,12.40,14.00,15.00,15.00,15.00,15.00,18.00,19.48,19.56,20.00,20.00,20.81,22.00,23.00,23.00,24.00,25.00,25.00,25.00,30.00,30.00,32.00,35.00,40.00,75.00 are the values sorted from the lowest to the highest.

By 'integer' we mean the integer portion and by decimal, the decimal portion (the part of the number following the decimal point) of a number.

First quartile formulas

If    is integer, the first quartile is

If    is not integer, the first quartile is interpolated using this formula:

Third quartile formulas

If    is integer, the third quartile is

If    is not integer, the third quartile is interpolated using this formula:

Q1= 9.365 AND Q3= 23.25

IQR= Q3-Q1= 23.25-9.365=13.885

I find Standard deviation by using excel funtion =STDEV and variance is square of standard deviation.