https://file.aiquickdraw.com/mathbot/file/1728975682649g3elutni.jpg

It seems that the image you have provided contains a word problem and a frequency table related to sales data at a grocery store between 10 PM and 6 AM. Here's a breakdown of the information and how we can address it:

### Problem Overview:
The manager at a grocery store is tracking sales to understand how much shoppers typically spend between 10 PM and 6 AM. The registers are programmed to record every 20th purchase, and they collect 21 data points. These are summarized in a frequency table showing the range of total bills for shoppers.

### Frequency Table (from the image):
- **$1–$20**: 3 shoppers
- **$21–$40**: 7 shoppers
- **$41–$60**: 5 shoppers
- **$61–$80**: 3 shoppers
- **$81–$100**: 2 shoppers
- **$101–$120**: 0 shoppers
- **$121–$140**: 0 shoppers
- **$141–$160**: 1 shopper

There are also **four additional sales** recorded:
- $132, $38, $60, and $148.

### What to Do:
Since the prompt asks for the "typical amount shoppers spend," the question is likely asking for some measure of central tendency (mean, median, or mode). Based on the frequency table and the additional sales, here's what can be done:

#### Step 1: Update the Frequency Table
We need to incorporate the four additional sales into the frequency table:
- **$132**: Falls in the $121–$140 range.
- **$38**: Falls in the $21–$40 range.
- **$60**: Falls in the $41–$60 range.
- **$148**: Falls in the $141–$160 range.

After including these:
- **$1–$20**: 3 shoppers
- **$21–$40**: 8 shoppers
- **$41–$60**: 6 shoppers
- **$61–$80**: 3 shoppers
- **$81–$100**: 2 shoppers
- **$101–$120**: 0 shoppers
- **$121–$140**: 1 shopper → 2 shoppers (after adding $132)
- **$141–$160**: 1 shopper → 2 shoppers (after adding $148)

#### Step 2: Identify the Typical Amount
There are 25 total data points now (21 + 4). We can find:
- **Mode**: This is the most frequent range, which is **$21–$40** (with 8 shoppers).
- **Median**: This requires sorting the data to find the middle value. With 25 data points, the median will be the 13th value. Based on the updated frequency table, the median lies in the **$21–$40** range.
- **Mean**: To calculate the mean, you would need to multiply each frequency by the midpoint of the ranges, sum them, and divide by 25.

The most common or "typical" value in this context is likely **$21–$40**, based on the mode and the median.

Would you like further details on any specific calculations or concepts?

### Follow-Up Questions:
1. How is the median calculated from grouped frequency data?
2. What is the exact mean value from this dataset?
3. How would the mode be interpreted in this context?
4. Can you explain how adding the four additional sales affects the median?
5. What if the manager used a different sampling method—how might that impact the result?

### Tip:
For grouped data, the **median** is often more reliable than the **mean** when outliers (like very high or low values) could skew the average.

A grocery store manager is tracking sales between 10 PM and 6 AM to find how much shoppers typically spend. The manager programs the registers to track every 20th purchase until they gather 21 data points. A frequency table of total bills is provided, and four additional sales amounts are recorded.

Learn how to analyze a frequency table to find the typical spending of grocery store shoppers between 10 PM and 6 AM. This problem focuses on statistical concepts like mean, median, mode, and frequency distribution with 25 data points. Suitable for students in Grades 8-10.

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