The government has sought to win the fight over its proposed tax cuts by suggesting it is really a tax cut for middle income earners. But despite assistance from some pretty dire reporting, Treasury’s own figures highlight just how greatly the tax cut is weighted towards high-income earners and those earning far more than the incomes of middle Australia.

Before the budget I wrote that the government would likely attempt to sell its budget by misleadingly referring to average income earners as middle Australia. But even I didn’t think we’d be at the point where someone on $200,000 would be considered middle income.

“Average” sounds like it is the middle – an “average Australian” sounds like someone who is typical of Australians and “average income” sounds like a typical income. It is why, for example, Malcolm Turnbull in question time on Wednesday referred to his tax plan by saying it would help “middle income earners” and that “middle Australia will benefit from this”.

But average earnings – especially average full-time earnings – are not what is earned by “middle Australia”.

Always remember – average full-time earnings are higher than average earnings, and average earnings are higher than median earnings.

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Current average full-time annual earnings are $81,531, but median annual earnings for a full-time worker are just $65,577:

The median income for all workers – that is, the amount at which half earn more and half earn less – is just $52,988.

And yet last week in the Australian we were told that “Turnbull’s tax plan will target the middle class” and that “the bulk of the tax benefit received would come from abolishing the 37% tax bracket and would go almost entirely to middle-income earners on wages of $120,000 to $200,000”.

Please.

The Australian suggested this was the case because of “Treasury analysis of wage data” that shows someone on an income of $120,000 in 2024-25 “would be considered the average wage equivalent to $84,600 in today’s terms” and that “a salary of $158,730 in 2017-18 would be $200,000 in 2024-25”. This would happen if wages grew by 3.5% each year after 2020-21.

That is absurd enough, but there is no reality in which an Australian worker on $120,000, let alone $200,000, can be classed as a middle-income earner.

It is utterly misleading to suggest that someone on $84,600 is middle-income – let alone someone on $158,730.

We know from the most recent taxation statistics that someone with a taxable income of $84,000 puts them in the top 25% and someone earning $158,000 is in the top 5%:

The AFR also got in on this absurdity, suggesting “wage rises will make $200k a middle income” and that “the chief beneficiaries of the third stage of the government’s income tax cuts will be earning up to $200,000 but they will be classified as middle-income earners by the time the cuts are delivered”.

We’ve reached a pretty awful place where someone earning nearly twice as much as the average full-time wage and three times the median wage is being called “middle-income”.

To be fair, someone on the actual median income of $52,988 will one day earn $200,000 – in 2056-57. And at that time, the AFR’s version of the median-income earner will be on $615,875:

On Wednesday the pitch was changed to refer to workers such as police officers and teachers (occupations conservative media governments always love, except when they are conducting industrial action to get a pay rise) and bizarrely a “forklift driver”.

The Australian suggested that a “forklift driver/excavator would pay almost $4,000 more a year in tax under Labor on a salary estimated at the most qualified level to be $164,331 in 2024-25”.

Such a salary would be news to most forklift drivers.

In the latest tax statistics, the median income for forklift drivers in 2015-16 was $48,622, and for an excavator operator the median income in 2015-16 was just $63,300.

On the Australian’s list of presumably middle-income earners was “school principal from the ACT”. In 2015-16 those principals had a median income of $131,692 – putting them in the top 8% all of taxpayers.

The government needs to push this line, of course, because those on the actual median income will not get to $120,000 until 2041-42 (assuming that wonderful 3.5% wage growth!).

On Tuesday the Treasury released new data during a Senate estimates hearing that tried to suggest the benefits of the tax plan would go to middle income earners. But it only serves to reinforce how much the plan benefits higher income earners and how the cost of those high income tax cuts dwarfs the rest.

By 2024-25, once the entire set of tax cuts go through, those on $200,000 would receive a tax cut of 3.6%, compared with what they pay now, whereas those on $70,000 (which will be the median income by then) get a cut of just 0.8%:

The tax cut is actually awful for “middle Australia”. Median income earners get a smaller tax cut than low-income earners and a very much smaller one than high-income earners.

And then we get to the cost – which is now up to $144bn out to the end 2028-29.

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The biggest cost to the budget over that time is the $41bn to raise the 19% threshold to $41,000. But that is planned to be done in 2022, and thus its cost covers seven years. The $33bn spent to remove the 32.5% tax bracket occurs over just five years – meaning on average it will cost the budget $6.6bn a year:

From 2024-25 all the tax cuts combined will reduce revenue by an average of $21.8bn a year, but $13.5bn – or 62% – of that is for tax cuts overwhelmingly for those earning over $120,000.

And how will the government pay for that $22bn cut to revenue?

This is the problem with misleading talk about who benefits, because when it comes to paying for it, you can bet the ones who will feel the effects of reduced services will be those who actually are part of middle Australia.

• Greg Jericho is a Guardian Australia columnist