Question

the tables below show the numbers of birds in different cages in two different pet shops.

pet shop #1
\

$$\begin{tabular}{|c|c|} \\hline cage & number of birds \\\\ \\hline 1 & 14 \\\\ \\hline 2 & 18 \\\\ \\hline 3 & 18 \\\\ \\hline 4 & 26 \\\\ \\hline 5 & 9 \\\\ \\hline \\end{tabular}$$

pet shop #2
\

$$\begin{tabular}{|c|c|} \\hline cage & number of birds \\\\ \\hline 1 & 20 \\\\ \\hline 2 & 22 \\\\ \\hline 3 & 19 \\\\ \\hline 4 & 30 \\\\ \\hline 5 & 18 \\\\ \\hline \\end{tabular}$$

what is the difference between the means of the numbers of birds per cage between the two shops?

a. 21.8
b. 17
c. 2.4
d. 4.8

Explanation:

Calculate the mean for Pet Shop #1

$$ \text{Sum}_1 = 14 + 16 + 18 + 26 + 9 = 83 $$

$$ \text{Mean}_1 = \frac{83}{5} = 16.6 $$

Calculate the mean for Pet Shop #2

$$ \text{Sum}_2 = 20 + 22 + 19 + 30 + 18 = 109 $$

$$ \text{Mean}_2 = \frac{109}{5} = 21.8 $$

Find the difference between the means

$$ \text{Difference} = 21.8 - 16.6 = 5.2 $$

Wait, let me re-read the values from the table carefully.
Pet Shop #1:
Cage 1: 14
Cage 2: 16
Cage 3: 18
Cage 4: 26
Cage 5: 9
Sum = 14 + 16 + 18 + 26 + 9 = 83. Mean = 16.6.

Pet Shop #2:
Cage 1: 20
Cage 2: 22
Cage 3: 19
Cage 4: 30
Cage 5: 18
Sum = 20 + 22 + 19 + 30 + 18 = 109. Mean = 21.8.

Let's check the options:
A. 21.8
B. 17
C. 2.4
D. 4.8

Let me re-examine the image values.
Pet Shop #1:
Cage 1: 14
Cage 2: 16
Cage 3: 18
Cage 4: 26
Cage 5: 9
Wait, is Cage 5 in Pet Shop #1 a 9? Yes, it looks like 9.
Is Cage 2 in Pet Shop #1 16? Yes.
Is Cage 4 in Pet Shop #1 26? Yes.
Is Cage 3 in Pet Shop #1 18? Yes.
Is Cage 1 in Pet Shop #1 14? Yes.
Sum = 14 + 16 + 18 + 26 + 9 = 83. Mean = 16.6.

Pet Shop #2:
Cage 1: 20
Cage 2: 22
Cage 3: 19
Cage 4: 30
Cage 5: 18
Sum = 20 + 22 + 19 + 30 + 18 = 109. Mean = 21.8.

Difference = 21.8 - 16.6 = 5.2.
Wait, is 4.8 an option? Yes, D is 4.8.
How could the difference be 4.8?
If Mean_1 was 17, then 21.8 - 17 = 4.8.
Let's check if Sum_1 could be 85:
If Cage 5 was 11: 14 + 16 + 18 + 26 + 11 = 85. Mean = 17.
Looking closely at Cage 5 of Pet Shop #1, it is "9".
Wait, let's look at Cage 5 of Pet Shop #1 again. Is it "9"? Yes, it is a single digit "9".
Wait, let's look at Cage 2 of Pet Shop #1. Is it "16"? Yes.
Let's look at Cage 3 of Pet Shop #1. Is it "18"? Yes.
Let's look at Cage 4 of Pet Shop #1. Is it "26"? Yes.
Let's look at Cage 1 of Pet Shop #1. Is it "14"? Yes.
What if Cage 5 of Pet Shop #1 is "11"? No, it is clearly "9".
Wait, what if Cage 5 of Pet Shop #2 is "18"?
Let's check: 20 + 22 + 19 + 30 + 18 = 109. Mean = 21.8.
What if Cage 5 of Pet Shop #2 is "16"?
20 + 22 + 19 + 30 + 16 = 107. Mean = 21.4.
21.4 - 16.6 = 4.8.
Looking at Cage 5 of Pet Shop #2, it is "18".
Wait, let's recalculate:
If Mean of Pet Shop #2 is 21.8 (which is Option A).
If the question asks "What is the difference between the means...", and one of the means is 21.8, then the other mean must be calculated.
If the difference is 4.8:
\(21.8 - \text{Mean}_1 = 4.8 \implies \text{Mean}_1 = 17\).
If \(\text{Mean}_1 = 17\), then the sum for Pet Shop #1 must be \(17 \times 5 = 85\).
Our sum was 83.
Let's look at the numbers for Pet Shop #1 again:
14, 16, 18, 26, 9.
Wait, is Cage 2 "18"?
Ah, Cage 2 is "18" and Cage 3 is "18"?
Let's look at Cage 2: "18".
Let's look at Cage 3: "18".
Yes! Both Cage 2 and Cage 3 have "18".
Let's sum them with 18 instead of 16:
14 + 18 + 18 + 26 + 9 = 85.
Indeed, the digit in Cage 2 is "18", not "16".
Let's recalculate with \(\text{Sum}_1 = 85\):

$$ \text{Mean}_1 = \frac{85}{5} = 17 $$

$$ \text{Difference} = 21.8 - 17 = 4.8 $$

This perfectly matches Option D.

Answer:

• (A) 21.8
• (B) 17
• (C) 2.4
• (D) 4.8 (Correct answer)