Complete the table below. Using the information on the completed table above, solve for the following: Use the spaces for your working out (a) Mean of the grouped data (b) Median of the grouped data (c) Mode of the grouped data (d) Range of the grouped data

Okay, Shasha, let's tackle this grouped data problem. There's an inconsistency in the first row of the table provided (the given Midpoint (M) and f(M) don't match the frequency (f) or the class interval). I will proceed by calculating the Midpoint (M) for each class interval using the standard formula $M = \frac{\text{lower limit} + \text{upper limit}}{2}$ and then calculate $f(M)$ accordingly. I will use these consistent values to complete the table and solve the subsequent questions.

C2. Complete the table below:

Step 1: Calculate the Midpoint (M) for each class interval.

• For $37-38$: $M = \frac{37+38}{2} = 37.5$
• For $39-40$: $M = \frac{39+40}{2} = 39.5$
• For $41-42$: $M = \frac{41+42}{2} = 41.5$
• For $43-44$: $M = \frac{43+44}{2} = 43.5$
• For $45-46$: $M = \frac{45+46}{2} = 45.5$
• For $47-48$: $M = \frac{47+48}{2} = 47.5$
• For $49-50$: $M = \frac{49+50}{2} = 49.5$

Step 2: Calculate $f(M)$ for each row by multiplying Frequency (f) by Midpoint (M).

• For $37-38$: $f(M) = 3 \times 37.5 = 112.5$
• For $39-40$: $f(M) = 3 \times 39.5 = 118.5$
• For $41-42$: $f(M) = 3 \times 41.5 = 124.5$
• For $43-44$: $f(M) = 4 \times 43.5 = 174.0$
• For $45-46$: $f(M) = 8 \times 45.5 = 364.0$
• For $47-48$: $f(M) = 4 \times 47.5 = 190.0$
• For $49-50$: $f(M) = 3 \times 49.5 = 148.5$

Step 3: Calculate the total frequency ($N$) and the sum of $f(M)$ ($\sum fM$).

• $N = 3+3+3+4+8+4+3 = 28$
• $\sum fM = 112.5 + 118.5 + 124.5 + 174.0 + 364.0 + 190.0 + 148.5 = 1232.0$

Here is the completed table:

Class Interval	Frequency (f)	Midpoint (M)	f(M)
37-38	3	37.5	112.5
39-40	3	39.5	118.5
41-42	3	41.5	124.5
43-44	4	43.5	174.0
45-46	8	45.5	364.0
47-48	4	47.5	190.0
49-50	3	49.5	148.5
N=	28		$\sum fM=$ 1232.0

Now, using the information from the completed table: