Question

2 the data set represents the number of eggs produced by a small group of chickens each day for 10 days. 7 7 7 7 7 8 8 8 8 9 select all the values that could represent the typical number of eggs produced in a day. a 7.5 eggs b 7.6 eggs c 7.7 eggs d 8 eggs e 9 eggs 3 from unit 1, lesson 2 the dot - plot displays the lengths of pencils (in inches) used by students in a class. length (inches) what is the mean? 4 from unit 1, lesson 2 the histogram represents ages of 39 people at a store that sells childrens clothes. which interval contains the median? a the interval from 0 to 5 years. b the interval from 5 to 10 years. c the interval from 10 to 15 years. d the interval from 15 to 20 years.

Explanation:

Question 2

Step1: Calculate the mean

The data set is \(7,7,7,7,7,8,8,8,8,9\). The sum of the data is \(7\times5 + 8\times4+9\times1=35 + 32+9 = 76\). There are \(n = 10\) data - points. The mean \(\bar{x}=\frac{76}{10}=7.6\).

Step2: Find the mode

The mode is the most frequently - occurring value. Here, the mode is \(7\) (occurs \(5\) times) and \(8\) (occurs \(4\) times).

Step3: Determine the median

Arrange the data in ascending order: \(7,7,7,7,7,8,8,8,8,9\). Since \(n = 10\) (an even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. The \(\frac{10}{2}=5\)th and \((\frac{10}{2}+1)=6\)th values are \(7\) and \(8\) respectively, so the median is \(\frac{7 + 8}{2}=7.5\).
The values that could represent the typical number of eggs produced in a day are the mean, median and mode. So the answers are A. 7.5 eggs, B. 7.6 eggs, D. 8 eggs.

Question 3

Step1: Count the number of data - points and their values from the dot - plot

There is \(1\) dot at \(5\), \(2\) dots at \(5.5\), \(4\) dots at \(6\), \(2\) dots at \(6.5\) and \(1\) dot at \(7\). The sum of the data is \(5\times1+5.5\times2 + 6\times4+6.5\times2+7\times1=5+11 + 24+13+7=60\). The total number of data - points \(n=1 + 2+4+2+1 = 10\).

Step2: Calculate the mean

The mean \(\bar{x}=\frac{60}{10}=6\) inches.

Step1: Find the position of the median

There are \(n = 39\) data - points. The median is the \(\frac{n + 1}{2}=\frac{39+1}{2}=20\)th value when the data is arranged in ascending order.

Step2: Cumulative frequency analysis

The cumulative frequency for the interval \(0 - 5\) is \(10\). The cumulative frequency for the interval \(0 - 10\) is \(10 + 8=18\). The cumulative frequency for the interval \(0 - 15\) is \(18+5 = 23\). Since the \(20\)th value falls within the interval where the cumulative frequency first exceeds \(20\), the median is in the interval from \(10\) to \(15\) years.

Answer:

6 inches

Question 4