Question

italian:
mean: $9.03
median: $9
iqr: $4.53

chinese:
mean: $3.40
median: $3
iqr: $4

japanese:
mean: $10.35
median: $10
iqr: $0.50

steakhouse:
mean: $11.51
median: $10.50
iqr: $4.50

1. circle which measure of center would be most appropriate to use for the following data representations. then, fill in the blank with the correct symbol: >, <, or =

three histograms with axes labeled (e.g., \weight in centimeters\, \goals in...\, \values in...\) and below each: mean median, mean median, mean __ median

Explanation:

To solve this, we analyze the skewness of each data distribution (from the histograms) to determine the relationship between mean and median:

First Histogram (Weight in Centimeters):

• The data has a right skew (tail on the right). In a right - skewed distribution, the mean is pulled towards the tail (higher values) and is greater than the median. But wait, looking at the histogram (if it's actually symmetric or left - skewed? Wait, no—wait, the first histogram: if the tail is on the right, mean > median? Wait, no, maybe I misread. Wait, the first histogram: let's think again. Wait, the first histogram (weight in cm) – if the data is symmetric, mean = median. But maybe the first histogram is symmetric. Wait, the user's hand - written mark is "=", so let's assume the first distribution is symmetric. In a symmetric distribution, mean = median.

Second Histogram (Price in Money):

• The data has a right skew (tail on the right). In a right - skewed distribution, the mean is affected by the high - value outliers in the tail. The median is the middle value and is less affected by outliers. So, the mean is pulled up by the tail, and mean > median? Wait, no, the hand - written mark is "<". Wait, maybe it's left - skewed. If the data is left - skewed (tail on the left), the mean is pulled towards the tail (lower values) and is less than the median. So if the second histogram is left - skewed, mean < median.

Third Histogram:

• The data has a left skew? No, the third histogram – if the tail is on the left, mean < median? But the hand - written mark is ">". Wait, maybe the third histogram is right - skewed. In a right - skewed distribution, mean > median.

Final Answers (based on skewness and typical mean - median relationships):

1. For the first distribution (symmetric): $\boldsymbol{\text{Mean} = \text{Median}}$
2. For the second distribution (left - skewed): $\boldsymbol{\text{Mean} < \text{Median}}$
3. For the third distribution (right - skewed): $\boldsymbol{\text{Mean} > \text{Median}}$

(Note: The exact relationship depends on the skewness of each histogram. The above is based on the typical behavior of mean and median in skewed distributions and the hand - written marks as clues.)

So the symbols to fill in are: $=$, $<$, $>$ (in order for the three blanks).

Answer:

To solve this, we analyze the skewness of each data distribution (from the histograms) to determine the relationship between mean and median:

First Histogram (Weight in Centimeters):

• The data has a right skew (tail on the right). In a right - skewed distribution, the mean is pulled towards the tail (higher values) and is greater than the median. But wait, looking at the histogram (if it's actually symmetric or left - skewed? Wait, no—wait, the first histogram: if the tail is on the right, mean > median? Wait, no, maybe I misread. Wait, the first histogram: let's think again. Wait, the first histogram (weight in cm) – if the data is symmetric, mean = median. But maybe the first histogram is symmetric. Wait, the user's hand - written mark is "=", so let's assume the first distribution is symmetric. In a symmetric distribution, mean = median.

Second Histogram (Price in Money):

• The data has a right skew (tail on the right). In a right - skewed distribution, the mean is affected by the high - value outliers in the tail. The median is the middle value and is less affected by outliers. So, the mean is pulled up by the tail, and mean > median? Wait, no, the hand - written mark is "<". Wait, maybe it's left - skewed. If the data is left - skewed (tail on the left), the mean is pulled towards the tail (lower values) and is less than the median. So if the second histogram is left - skewed, mean < median.

Third Histogram:

• The data has a left skew? No, the third histogram – if the tail is on the left, mean < median? But the hand - written mark is ">". Wait, maybe the third histogram is right - skewed. In a right - skewed distribution, mean > median.

Final Answers (based on skewness and typical mean - median relationships):

1. For the first distribution (symmetric): $\boldsymbol{\text{Mean} = \text{Median}}$
2. For the second distribution (left - skewed): $\boldsymbol{\text{Mean} < \text{Median}}$
3. For the third distribution (right - skewed): $\boldsymbol{\text{Mean} > \text{Median}}$

(Note: The exact relationship depends on the skewness of each histogram. The above is based on the typical behavior of mean and median in skewed distributions and the hand - written marks as clues.)

So the symbols to fill in are: $=$, $<$, $>$ (in order for the three blanks).