Question

ms. chowdhury/algebra 1/term 1,3 name: marking period 1 (fall) homework on data representations do your personal best. this homework will be graded towards your assignment section (35%) 1. a class of 20 students was surveyed to determine the number of pets each student owned. the data are represented in the dot - plot below. which statement about the data is correct? (1) the mean and the median are the same. (2) the median and the mode are the same. (3) the mean and the mode are the same. (4) the mean, median, and mode are all the same. 2. the histogram represents ages of 40 people at a store that sells childrens clothes. which interval contains the median? circle your response. 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. 3. name each of the following distributions. (symmetric, skewed, uniform, bell - shaped, bimodal). write the name next to each image.

Explanation:

Step1: Analyze question 1

For the dot - plot of number of pets of 20 students:
First, find the mode. The mode is the most frequently occurring value. From the dot - plot, assume the number of dots for each value of number of pets. Let's say the mode is 2 (if it has the most dots).
To find the median, since \(n = 20\) (an even number of data points), the median is the average of the \(\frac{n}{2}=10\)th and \((\frac{n}{2}+ 1)=11\)th ordered data points.
To find the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(x_{i}\) is the number of pets for each student and \(n = 20\). After calculating, we find that the median and mode are the same.

Step2: Analyze question 2

For a histogram with \(n = 40\) data points. Since \(n = 40\) (an even number), the median is the average of the 20th and 21st ordered data points.
We need to find the cumulative frequencies for each interval. Starting from the first interval, we add up the frequencies. After calculating the cumulative frequencies for each interval \(0 - 5\), \(5 - 10\), \(10 - 15\), \(15 - 20\) etc., we find that the 20th and 21st data points fall in the \(10 - 15\) years interval.

Step3: Analyze question 3

A: The distribution is symmetric as it is evenly balanced on both sides of the center.
B: The distribution is skewed (right - skewed if the tail is on the right side) as one side has more spread out data points.
C: The distribution is uniform as the data points are evenly distributed across the values.
D: The distribution is bell - shaped as it has a single peak and is symmetric around the peak.

Answer:

1. (2)
2. C. The interval from 10 to 15 years.
3. A. Symmetric

B. Skewed
C. Uniform
D. Bell - shaped