4. the dot plot displays the number of bushes in the yards for houses in a neighborhood. state the mode and…

4.

Explanation:

Step1: Find the mode

The mode is the value that appears most frequently. Looking at the dot - plot (not shown here but conceptually), we count the frequency of each value.

Step2: Find the median

First, we need to know the total number of data points. Then, if the number of data points $n$ is odd, the median is the $\left(\frac{n + 1}{2}\right)$-th ordered value. If $n$ is even, the median is the average of the $\frac{n}{2}$-th and $\left(\frac{n}{2}+1\right)$-th ordered values.

Answer:

Mode: <Value with highest frequency in the dot - plot> Median: <Calculated value based on the number of data points and their order>

5.

Explanation:

Step1: Order the data

The data set is $4,5,5,5,6,6,6,6,7,7,7,7,7.5,7.5,8,8,8.5,8.5,9$. After ordering, it remains the same as it is already in ascending order.

Step2: Find the five - number summary

1. Minimum: The smallest value is $4$.
2. First quartile ($Q_1$): The lower half of the data is $4,5,5,5,6,6,6,6,7$. The median of this lower half is the 5th value, so $Q_1 = 6$.
3. Median ($Q_2$): Since $n = 19$ (odd), the median is the $\left(\frac{19 + 1}{2}\right)=10$ - th value, so $Q_2=7$.
4. Third quartile ($Q_3$): The upper half of the data is $7.5,7.5,8,8,8.5,8.5,9$. The median of this upper half is the 5th value of the upper - half, so $Q_3 = 8$.
5. Maximum: The largest value is $9$.

Step3: Draw the box - plot

Draw a number line that includes the range from the minimum to the maximum. Draw a box from $Q_1$ to $Q_3$, draw a vertical line inside the box at $Q_2$, and draw whiskers from the box to the minimum and maximum values.

Answer:

A box - plot with minimum at $4$, $Q_1$ at $6$, median at $7$, $Q_3$ at $8$, and maximum at $9$.

6.

a.

Explanation:

Step1: Draw a number line

Draw a number line that includes all the values in the data set, from $92$ to $119$.

Step2: Plot the dots

For each value in the data set $92,95,95,95,98,100,100,100,103,105,105,111,112,115,115,116,117,117,118,119,119,119,119,119,119$, place a dot above the corresponding number on the number line.

Answer:

A dot - plot with dots placed above the values on a number line ranging from $92$ to $119$ according to the frequency of each value in the data set.

b.

Explanation:

Step1: Create a frequency table

1. For the interval $90 - 100$:
   • Count the number of values in the data set $92,95,95,95,98,100,100,100,103,105,105,111,112,115,115,116,117,117,118,119,119,119,119,119,119$ that fall in this interval. The values are $92,95,95,95,98$, so the frequency is $5$.
2. For the interval $100 - 110$:
   • The values are $100,100,100,103,105,105$, so the frequency is $6$.
3. For the interval $110 - 120$:
   • The values are $111,112,115,115,116,117,117,118,119,119,119,119,119,119$, so the frequency is $14$.

Step2: Draw the histogram

On the x - axis, label the intervals $90 - 100$, $100 - 110$, and $110 - 120$. On the y - axis, label the frequency. 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