Please help me find the average number (a survey of 10000 people)

Hi! I conducted a survey of 10000 people that measured how much value they put on something. They were given 9 options and each option has a range. I was wondering what the average value was of the participants. Thank you! Here are the numbers:

A1	0-49		37.40%	374
A2	50-99		19.30%	193
A3	100-149		14.60%	146
A4	150-199		7.80%	78
A5	200-249		5.30%	53
A6	250-299		2.80%	28
A7	300-349		1.50%	15
A8	350-399		1.30%	13
A9	400+		10.00%	100

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TOTAL UNIQUE RESPONDENTS
1000
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There isn't enough information provided to get an exact average. For example, of the 374 people who selected the 0-49 range, we don't know the mean value given by those 374 participants. They may have all given a 0 or all given a 49, or something in between.

You could estimate the overall average by supposing the mean in each range is the midpoint of that range and use a weighted average:

\(\displaystyle \displaystyle \overline{x}\approx\frac{1}{1000}\sum_{k=1}^{9} \left(P_k\frac{R_{k_{\min}}+R_{k_{\max}}}{2}\right)\)

Where:

\(\displaystyle P_k\) = the number of participants in the \(\displaystyle k\)th range.

\(\displaystyle R_{k_{\min}}\) = the lower bound of the \(\displaystyle k\)th range.

\(\displaystyle R_{k_{\max}}\) = the upper bound of the \(\displaystyle k\)th range.

Clarification

^{Thanks for the prompt response. I don't need an exact number so 0-49 would be 24.5 and 50-99 would be 74.5 etc. Not sure if that changes the equation.}

alexdott said:

^{Thanks for the prompt response. I don't need an exact number so 0-49 would be 24.5 and 50-99 would be 74.5 etc. Not sure if that changes the equation.}

Click to expand...

Yes, this is what I proposed.