QuestionGiven frequency distributions for $X$ and $Y$ , create histograms, find relative frequencies, and compare averages.

Studdy Solution

STEP 1

Assumptions1. The frequency distribution of $X$ and $Y$ is given in the table. . The values of $X$ and $Y$ are discrete.
3. The frequencies are absolute, not relative.

STEP 2

To draw a histogram of frequencies for $X$ , we need to represent the values of $X$ on the x-axis and their corresponding frequencies on the y-axis.

STEP 3

Similarly, to draw a histogram of relative frequencies for $Y$ , we first need to calculate the relative frequencies. The relative frequency of a value is the absolute frequency of that value divided by the total frequency.
$Relative\, Frequency\, of\, Y = \frac{Frequency\, of\, Y}{Total\, Frequency\, of\, Y}$

STEP 4

To find the relative frequencies for $X$ , we apply the same formula as in3, but for $X$ .
$Relative\, Frequency\, of\, X = \frac{Frequency\, of\, X}{Total\, Frequency\, of\, X}$

STEP 5

To find the percentage that $X$ is at least2, we need to sum the frequencies of $X$ for values2,3, and4, and then divide by the total frequency of $X$ , and multiply by100 to convert to a percentage.
$Percentage\, that\, X\, is\, at\, least\,2 = \frac{Frequency\, of\, X\, for\, values\,2,\,3,\, and\,4}{Total\, Frequency\, of\, X} \times100$

STEP 6

To find the percentage that $Y=2$ , we divide the frequency of $Y$ for value2 by the total frequency of $Y$ , and multiply by100 to convert to a percentage.
$Percentage\, that\, Y=2 = \frac{Frequency\, of\, Y\, for\, value\,2}{Total\, Frequency\, of\, Y} \times100$

STEP 7

To find which variable, $X$ or $Y$ , has a higher average value, we calculate the average (mean) of each variable. The mean of a variable is the sum of the product of each value and its frequency, divided by the total frequency.
$Mean\, of\, X = \frac{\sum (Value\, of\, X \times Frequency\, of\, X)}{Total\, Frequency\, of\, X}$ $Mean\, of\, Y = \frac{\sum (Value\, of\, Y \times Frequency\, of\, Y)}{Total\, Frequency\, of\, Y}$ Then we compare the means of $X$ and $Y$ to see which is higher.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms