Compare the IQ and Number of Hours of TV watched per week.

Frequency Charts:

Boys

Girls

The mode IQ for girls is the same as boys, however the spread of IQ for boys is higher than for girls.

My sample shows that there will be more boys with an IQ of over 100 than girls.

Mean IQ:

Mean IQ for boys = 102

Mean IQ for girls = 101.1

Modal Class Interval IQ:

MCL IQ for boys = 100-105

MCL IQ for girls = 100-105

Median IQ:

Median IQ for boys = 100

Median IQ for girls = 103

Range of IQ:

Range of IQ for boys = 45

Range of IQ for girls = 37

The 3 averages all gave me different results. The mean stated that boys have a higher IQ; the MCI stated that they are equal and the median stated that the girls have a higher IQ. From this I can deduce that it is inconclusive, however boys’ and girls’ average IQ’s are roughly similar.

My sample suggests that 83% of boys have an IQ between 95 and 110, where as only 59% girls have an IQ between 95 and 100.

        All three averages of my sample state that boys watch more TV per week than girls and the sample for boys is less spread out.

My sample states that 34.5% of boys watch between 25 and 50 hours of TV per week, where as only 11.1% of girls do.

These conclusions are based on a sample and not the entire data. To determine whether my results are accurate I could repeat or extend the test.

Further Investigation:

Hypothesis:

There will be a better correlation between IQ and hours of TV watched per week if we consider boy and girls separately.

I will use the same sample as I have previously and represent the data in scatter diagrams.

Scatter Diagram for Boys and Girls:

From the two lines of best fit, I can predict that:

• A boy with an IQ of 90 will watch 30 hours of TV per week, whereas a girl with the same IQ will watch 22 hours of TV per week.
• A girl who watches 20 hours of TV per week will have an IQ of 93, whereas a boy who watches the same amount of TV will have an IQ of 103.

From the lines of best fit, I can obtain these equations:

If y represents hours of TV watched per week, and x represents IQ, then the equations are:

Boys only: y = -0.75x + 53

Girls only: y = -0.75x + 47

Combined Sample: y = -0.75x + 50

I can use these equations to make predictions when I know one of the 2 pieces of data, i.e. IQ if I know the no. of TV hours watched per week.

Example

If a boy watches 5 hours of TV per week:

    y = -0.75x + 53

So x = Y – 53

              -0.75

If y = 5 then                                        

X = 5 – 53   = 64

        -0.75

= 64

Using the equation from my line of best fit, I can predict that a boy who watches 5 hours of TV per week will have an IQ of 64.

The line of best fit is the closest estimation to the correlation of IQ and no. of TV hours watched per week. There are anomalous or irregular results, such as the boy with an IQ of 89 who watches 42 hours of TV per week. The line of best fit is a continuous relationship, though IQ is a discrete variable. Rounding IQ to the nearest integer makes my prediction less accurate.

Cumulative Frequency Graphs:    

 

The Curves show the trend towards higher IQ amongst for boys and girls. However the curve is a continuous measure of cumulative frequency, and IQ is a discrete variable. Therefore, it would be more appropriate to use a cumulative frequency graph on the Hours of TV watched.

I will now show a cumulative frequency graph for Number of Hours of TV watched per week.

Cumulative Frequency Chart for Hours of TV watched:

This Cumulative Frequency graph gives these readings:

 

The box and whisker diagrams show that the amount of TV watched between boys and girls is similar. However, the boys watch 12 minutes more per week.

The Median Amount of TV watched is:

Boys: 20

Girls: 14

The cumulative frequency graph shows that:

• 19/28 girls watch less TV than the median of boys.

• 23/29 boys watch more TV than the median of girls.

This means that, whilst in general, boys watch more TV; the evidence suggests that 39% of girls watch more than the median for boys.

Results:

The scatter diagrams did not show a very good correlation and neither did the averages nor Interquartile range. This may be because not enough samples were used. There is a possibility, if I had used 100 or more samples I would have found a correlation.

My hypothesis stated that people with higher IQ would watch less TV, or words to that effect. This was wrong, because on average girls watched less TV and boys were more intelligent.

I tried to reduce the limiting factors, by taking a stratified sample, rather than a random sample.