6. marsha was shopping for a new dishwasher and researched the different models she could afford. using…

6. marsha was shopping for a new dishwasher and researched the different models she could afford. using marshas frequency - distribution table, determine the median price for dishwashers.\nprice,p($) frequency,f\n250 2\n275 4\n280 1\n290 2\n310 6\n315 2\n320 1\n325 7\n330 1\n335 1\n340 1\n350 2\na. $317.50 b. $325.00\nc. $312.50 d. $308.33\n7. mckenzie found the correlation coefficient on a set of data to be - 0.20. which term best describes the correlation?\na. strong positive b. strong negative\nc. weak positive d. weak negative\n8. your income before all taxes are deducted is known as your\na. disposable income\nb. gross income\nc. discretionary income\nd. essential income\n9. which measure of central tendency should be used if there are outliers in the distribution?\na. mean\nb. median\nc. mode\nd. standard deviation\n10. a table that displays each possible value and the number of times that value occurs is known as a\na. count table\nb. cumulative relative frequency table\nc. relative frequency table\nd. frequency table\n11. a scatter plot is graphed with the time it takes a child to get dressed in the morning on the vertical axis and the child’s age in years on the horizontal axis. the graph shows a negative correlation because\na. the time increases as the age of the child increases.\nb. the time decreases as the age of the child increases.\nc. the time decreases as the age of the child decreases.

6. marsha was shopping for a new dishwasher and researched the different models she could afford. using marshas frequency - distribution table, determine the median price for dishwashers.\nprice,p($) frequency,f\n250 2\n275 4\n280 1\n290 2\n310 6\n315 2\n320 1\n325 7\n330 1\n335 1\n340 1\n350 2\na. $317.50 b. $325.00\nc. $312.50 d. $308.33\n7. mckenzie found the correlation coefficient on a set of data to be - 0.20. which term best describes the correlation?\na. strong positive b. strong negative\nc. weak positive d. weak negative\n8. your income before all taxes are deducted is known as your\na. disposable income\nb. gross income\nc. discretionary income\nd. essential income\n9. which measure of central tendency should be used if there are outliers in the distribution?\na. mean\nb. median\nc. mode\nd. standard deviation\n10. a table that displays each possible value and the number of times that value occurs is known as a\na. count table\nb. cumulative relative frequency table\nc. relative frequency table\nd. frequency table\n11. a scatter plot is graphed with the time it takes a child to get dressed in the morning on the vertical axis and the child’s age in years on the horizontal axis. the graph shows a negative correlation because\na. the time increases as the age of the child increases.\nb. the time decreases as the age of the child increases.\nc. the time decreases as the age of the child decreases.

Answer

Explanation:

Step1: Calculate total frequency

Sum all frequencies: $2 + 4+1 + 2+6+2 + 1+7+1+1+2= 29$. Since $n = 29$ (odd), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{29+ 1}{2}=15$ - th value.

Step2: Find cumulative frequencies

Start adding frequencies:

  • For price $250$, cumulative frequency is $2$.
  • For price $275$, cumulative frequency is $2 + 4=6$.
  • For price $280$, cumulative frequency is $6+1 = 7$.
  • For price $290$, cumulative frequency is $7+2 = 9$.
  • For price $310$, cumulative frequency is $9+6 = 15$. So the median price is $310$.

Step3: Calculate median for grouped - like data (using interpolation, although in this case we directly got the value)

(Not really needed as we found the value directly from cumulative frequencies, but for general method) Let $L$ be the lower limit of the median - class ($310$), $n$ be the total frequency ($29$), $F$ be the cumulative frequency of the class before the median - class ($9$), $f$ be the frequency of the median - class ($6$), and $w$ be the class - width (assumed $5$ here). The formula for median is $M = L+\frac{\frac{n}{2}-F}{f}\times w$. But as we found the value without interpolation, we can confirm the median is $310$.

Step4: For question 7

The correlation coefficient $r=- 0.20$. Since $|r|\lt0.3$, it is a weak correlation. And since $r\lt0$, it is a weak negative correlation. So the answer is d.

Step5: For question 8

Income before all taxes are deducted is called gross income. So the answer is b.

Step6: For question 9

The median is not affected by outliers as it is the middle - value. Mean is affected by outliers as it takes into account all values in the data - set. Mode is the most frequently occurring value and standard deviation measures the spread. So the answer is b.

Step7: For question 10

A table that displays each possible value and the number of times that value occurs is known as a frequency table. So the answer is d.

Step8: For question 11

A negative correlation means that as one variable increases, the other decreases. If the horizontal axis is the child's age and the vertical axis is the time to get dressed, a negative correlation means the time decreases as the age of the child increases. So the answer is b.

Answer:

  1. $310$
  2. d. Weak negative
  3. b. gross income
  4. b. median
  5. d. frequency table
  6. b. the time decreases as the age of the child increases.