PROBLEM 1 The (rounded) average price for a box of cookies obtained from randomly picked bakeries is listed below: 40 23 11 20 22 20 45 15 28 21 22 20 72 19 22 28 25 19 23 47 45 15 30 10 55 15 17 49 Construct a grouped frequency distribution and a cumulative frequency distribution with 6 classes. Note: give a brief explanation by specifying the covered steps. Grouped Frequency Distribution Step 1. Find Range Step 2. Compute classes’ width (always round-up; if the width computation results in an integer, round it up to the next integer) Step 3. Create class boundaries Cumulative Frequency Distribution Step 1. Find Range Step 2. Compute classes’ width Step 3. Find the frequencies and the corresponding percentage Use Excel to construct a Histogram. (Tools à Data Analysis à Histogram à for input range select the given values, for the bin range select the classes upper boundaries values à check Chart Output).
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
PROBLEM 1
The (rounded) average price for a box of cookies obtained from randomly picked bakeries is listed below:
40 23 11 20 22 20 45 15 28 21
22 20 72 19 22 28 25 19 23 47
45 15 30 10 55 15 17 49
- Construct a grouped frequency distribution and a cumulative frequency distribution with 6 classes.
Note: give a brief explanation by specifying the covered steps.
Grouped Frequency Distribution
Step 1. Find
Step 2. Compute classes’ width (always round-up; if the width computation results in an integer, round it up to the next integer)
Step 3. Create class boundaries
Cumulative Frequency Distribution
Step 1. Find Range
Step 2. Compute classes’ width
Step 3. Find the frequencies and the corresponding percentage
- Use Excel to construct a Histogram. (Tools à Data Analysis à Histogram à for input range select the given values, for the bin range select the classes upper boundaries values à check Chart Output).
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