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adell [148]
3 years ago
11

Determine the type of correlation that exists in the given data set. Age (years) 23 45 39 74 63 52 59 28 35 11 26 49 IQ 76 82 11

3 111 109 115 101 127 92 123 128 99 A. According to this data, there is a positive correlation between age and IQ. B. According to this data, there is a negative correlation between age and IQ. C. According to this data, there is no correlation between age and IQ. D. There is not enough information in this data to determine what type of correlation exists between age and IQ.

Mathematics
2 answers:
Lyrx [107]3 years ago
6 0

Answer:

B -0.104

Step-by-step explanation:

Step 1: Write the formula for correlation

r =    total xy

√Total x² x Total y²

Step 2: Make a table to calculate all values

Table is attached in the picture below

Step 3 : Solve

Mean of X = Total X/ Total number of X

                  = 507/12

                  = 106.33

Mean of Y = Total Y/ Total number of Y

                  = 1276/ 12  

                  = 42.25

r =    total xy

√Total x² x Total y²

r = -352.05/ √3656.25 x 3122.66698

r = -0.104

-0.104 is negative

This negative correlation means there is an inverse correlation between variables.

Kitty [74]3 years ago
6 0

Answer:

B. According to this data, there is a negative correlation between age and IQ.

Step-by-step explanation:

Correlation shows the strength of relation between two variables. The formula used to calculate correlation is:

Correlation(r) = \frac{Cov(x, y)}{\sigma_{x}\sigma_{y}}= \frac{E(x-\mu_{x})(y-\mu_{y})}{\sigma_{x}\sigma_{y}}

where, Cov(x,y) = Covariance of x and y

\sigma_{x} = standard deviation of x

\sigma_{y} = standard deviation of y

\mu_{x} = mean of x

\mu_{y} = mean of y

and, E denotes the Expectation.

The value of the correlation lies between -1 to +1.

If the value of correlation lies between -1 to 0 then it is known as a negative correlation.

and, If the value of correlation lies between 0 to 1 then it is known as a positive correlation.

Using the above formula of correlation we get Correlation (r) = -0.1225.

Thus, there is negative correlation between age and IQ.

We can also use a correlation calculator for getting the value of correlation.

Hence, option (B) is correct.

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Find the mean of the data summarized in the given frequency distribution . Compare the computed mean to the actual mean of 57.6
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The mean of the frequency distribution is 52.6° F. The computed mean of 52.6° F is lesser than the actual mean of 57.6° F.

<h3>What is the mean of a distribution?</h3>

The mean of the distribution can be defined as the average value of the distribution, It can be expressed as the total sum of all the observed values divided by the frequency of the distribution.

From the parameters given:

Low-temperature             Frequency

40 - 44                                    2

45 - 49                                    5

50 - 54                                    9

55 - 59                                    6

60 - 64                                    3

The first thing to do is to determine the class midpoint. The class midpoint is the sum of the class interval divided by 2.

The class midpoint of 40 - 44 is \mathbf{\dfrac{40 + 44}{2} = 42}

The class midpoint of 45 - 49 is \mathbf{\dfrac{45 + 49}{2} = 47}

The class midpoint of 50 - 54 is \mathbf{\dfrac{50 + 54}{2} = 52}

The class midpoint of 55 - 59 is \mathbf{\dfrac{55 + 59}{2} = 57}

The class midpoint of 60 - 64 is \mathbf{\dfrac{60 + 64}{2} = 62}

Now, the table can be represented as:

Low-temperature             Frequency          x  

40 - 44                                    2                   42

45 - 49                                    5                   47

50 - 54                                    9                   52

55 - 59                                    6                   57

60 - 64                                    3                   62

The mean can now be determined as follows:

\mathbf{\bar x = \dfrac{\sum fx}{\sum f }}

\mathbf{\bar x = \dfrac{(2 \times 42)+ (5 \times 47) + ( 9\times 52) +(6\times 57) + (3 \times 62)}{2 + 5 + 9 + 6 + 3 }}

\mathbf{\bar x = \dfrac{1315}{25}}

\mathbf{\bar x = 52.6}

Therefore, we can conclude that the mean of the frequency distribution is 52.6° F. The computed mean of 52.6° F. is lesser than the actual mean of 57.6° F

Learn more about the mean of frequency distribution here:

brainly.com/question/12269435

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