Math Problem Statement
To inspect manufacturing processes, companies typically examine samples of parts for deficiencies. One company that manufactures ballpoint pens selected samples of its manufactured pens on each of 10 days. The company recorded, for each sample, the number of defective pens in the sample. Here are their data.
17, 10, 5, 6, 26, 14, 27, 4, 21, 16
(a) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place.
(b) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable.
Solution
Let's analyze each part of the question:
Given Data
The recorded number of defective pens over 10 days is:
To make calculations easier, let's sort the dataLet's analyze each part of the question:
Given Data
The recorded number of defective pens over 10 days is:
To make calculations easier, let's sort the
(a) Median of the Data Set
The median is the middle value of an ordered data set. Since there are 10 values (an even number), the median will be the average of the two middle values.
The middle values are the 5th and 6th values in the sorted list:
- 5th value: 14
- 6th value: 16
So, the median is:
Answer (a): The median is 15.0.
(b) Mean of the Data Set
The mean is calculated by dividing the sum of all values by the number of values.
- Sum of all values: [ 4 + 5 +
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Math Problem Analysis
Mathematical Concepts
Statistics
Measures of Central Tendency
Mean
Median
Mode
Formulas
Median formula for an even set of values: (value at n/2 + value at (n/2) + 1) / 2
Mean formula: Sum of all values / Number of values
Mode definition: Most frequently occurring value(s)
Theorems
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Suitable Grade Level
Grades 7-10